the height of the pentagonal pyramid is 5. 70 meters
The formula for determining the volume of a regular pentagonal pyramid is given as;
V=5/12tan(54°)ha^2
Where
We have the volume to be;
volume = 82. 5 cubic centers
height = h
a = 5m
Substitute the values
[tex]82. 5 = \frac{5}{12}[/tex] × [tex]tan 54[/tex] × [tex]h[/tex] ×[tex]5^2[/tex]
[tex]82. 5 = 0. 42[/tex] × [tex]1. 3764[/tex] × [tex]25[/tex] × [tex]h[/tex]
Make 'h' subject of formula
[tex]h = \frac{82. 5}{14. 45}[/tex]
h = 5. 70 meters
The height of the pentagonal pyramid is 5. 70 meters
Thus, the height of the pentagonal pyramid is 5. 70 meters
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